Earth's crust may sway?

Question

1. Is it possible for Earth's crust to have a swaying movement, like non-anchored ships ?

2. Do mountains prevent that movement?

Answer 1

There is no evidence that the Earth's crust has a swaying or rocking motion analogous to a ship at sea.  You are thinking of the crust all wrong to imagine that it is floating on liquid.  The crust sits on top of the upper Mantle - which itself is made of rock.  But the rock making up the Mantle is under so much pressure from the weight of the rock above and is so hot from heat escaping the molten core, that it acts in a plastic manner, slowly flowing (kind of like Silly Putty) with convective heat currents from deep near the outer core up to the crust. While it is true that the crust is thicker below mountain chains, that extra crustal thickness is irrelevant to the movement of the plate on which they occur.